On Harmonic Theory in Flows

2003 ◽  
Vol 46 (4) ◽  
pp. 617-631 ◽  
Author(s):  
Hong Kyung Pak
Keyword(s):  
Contact Manifold ◽  
Natural Generalization ◽  
Basic Flow ◽  
Compact Manifolds ◽  
Cohomology Spaces ◽  
Special Case

AbstractRecently [8], a harmonic theory was developed for a compact contact manifold from the viewpoint of the transversal geometry of contact flow. A contact flow is a typical example of geodesible flow. As a natural generalization of the contact flow, the present paper develops a harmonic theory for various flows on compact manifolds. We introduce the notions of H-harmonic and H*-harmonic spaces associated to a Hörmander flow. We also introduce the notions of basic harmonic spaces associated to a weak basic flow. One of our main results is to show that in the special case of isometric flow these harmonic spaces are isomorphic to the cohomology spaces of certain complexes. Moreover, we find an obstruction for a geodesible flow to be isometric.

Existence and positivity of the limit in processes with a branching structure

1999 ◽  
Vol 36 (1) ◽  
pp. 132-138
Author(s):  
M. P. Quine ◽  
W. Szczotka
Keyword(s):  
Stochastic Process ◽  
Branching Process ◽  
Random Variables ◽  
Random Variable ◽  
Natural Generalization ◽  
Partial Sums ◽  
Urn Model ◽  
Special Case ◽  
Independent And Identically Distributed

We define a stochastic process {Xn} based on partial sums of a sequence of integer-valued random variables (K0,K1,…). The process can be represented as an urn model, which is a natural generalization of a gambling model used in the first published exposition of the criticality theorem of the classical branching process. A special case of the process is also of interest in the context of a self-annihilating branching process. Our main result is that when (K1,K2,…) are independent and identically distributed, with mean a ∊ (1,∞), there exist constants {cn} with cn+1/cn → a as n → ∞ such that Xn/cn converges almost surely to a finite random variable which is positive on the event {Xn ↛ 0}. The result is extended to the case of exchangeable summands.

Molecular replacement with multiple different models

2004 ◽  
Vol 37 (1) ◽  
pp. 159-161 ◽  
Author(s):  
Nicholas M. Glykos ◽  
Michael Kokkinidis
Keyword(s):  
Crystal Structure ◽  
Original Description ◽  
Natural Generalization ◽  
Divide And Conquer ◽  
Search Model ◽  
Molecular Replacement ◽  
Asymmetric Unit ◽  
Different Types ◽  
Replacement Problem ◽  
Special Case

Classical molecular replacement methods and the newer six-dimensional searches treat molecular replacement as a succession of sub-problems of reduced dimensionality. Due to their `divide-and-conquer' approach, these methods necessarily ignore (at least during their early stages) the very knowledge that a target crystal structure may comprise, for example, more than one copy of a search model, or several models of different types. An algorithm for a stochastic multi-dimensional molecular replacement search has been described previously and shown to locate solutions successfully, even in cases as complex as a 23-dimensional 4-body search. The original description of the method only dealt with a special case of molecular replacement, namely with the problem of placingncopies of only one search model in the asymmetric unit of a target crystal structure. Here a natural generalization of this algorithm is presented to deal with the full molecular replacement problem, that is, with the problem of determining the orientations and positions of a total ofncopies ofmdifferent models (withn≥m) which are assumed to be present in the asymmetric unit of a target crystal structure. The generality of this approach is illustrated through its successful application to a 17-dimensional 3-model problem involving one DNA and two protein molecules.

scholarly journals A Characterization of Balanced Episturmian Sequences

10.37236/951 ◽  
2007 ◽  
Vol 14 (1) ◽  
Author(s):  
Geneviève Paquin ◽  
Laurent Vuillon
Keyword(s):  
Natural Generalization ◽  
Periodic Sequences ◽  
Letter Alphabet ◽  
Sturmian Sequences ◽  
Special Case

It is well-known that Sturmian sequences are the non ultimately periodic sequences that are balanced over a 2-letter alphabet. They are also characterized by their complexity: they have exactly $(n+1)$ distinct factors of length $n$. A natural generalization of Sturmian sequences is the set of infinite episturmian sequences. These sequences are not necessarily balanced over a $k$-letter alphabet, nor are they necessarily aperiodic. In this paper, we characterize balanced episturmian sequences, periodic or not, and prove Fraenkel's conjecture for the special case of episturmian sequences. It appears that balanced episturmian sequences are all ultimately periodic and they can be classified in 3 families.

scholarly journals A new proof of a generalization of Gerzon’s bound

2020 ◽  
Author(s):  
Gábor Hegedüs
Keyword(s):  
Linear Algebra ◽  
Upper Bound ◽  
Natural Generalization ◽  
Simple Application ◽  
Special Case

AbstractIn this paper we give a short, new proof of a natural generalization of Gerzon’s bound. This bound improves the Delsarte, Goethals and Seidel’s upper bound in a special case. Our proof is a simple application of the linear algebra bound method.

scholarly journals ON ITERATED TRANSLATED POINTS FOR CONTACTOMORPHISMS OF ℝ2n+1 AND ℝ2n × S1

2012 ◽  
Vol 23 (02) ◽  
pp. 1250042 ◽  
Author(s):  
SHEILA SANDON
Keyword(s):  
Fixed Points ◽  
Critical Points ◽  
Generating Functions ◽  
Contact Manifold ◽  
Contact Form ◽  
Compactly Supported ◽  
Partial Contact ◽  
Legendrian Submanifolds ◽  
Special Case

A point q in a contact manifold is called a translated point for a contactomorphism ϕ with respect to some fixed contact form if ϕ(q) and q belong to the same Reeb orbit and the contact form is preserved at q. The problem of existence of translated points has an interpretation in terms of Reeb chords between Legendrian submanifolds, and can be seen as a special case of the problem of leafwise coisotropic intersections. For a compactly supported contactomorphism ϕ of ℝ2n+1 or ℝ2n × S1 contact isotopic to the identity, existence of translated points follows immediately from Chekanov's theorem on critical points of quasi-functions and Bhupal's graph construction. In this article we prove that if ϕ is positive then there are infinitely many nontrivial geometrically distinct iterated translated points, i.e. translated points of some iteration ϕk. This result can be seen as a (partial) contact analog of the result of Viterbo on existence of infinitely many iterated fixed points for compactly supported Hamiltonian symplectomorphisms of ℝ2n, and is obtained with generating functions techniques.

Steady finite motions of a conducting liquid

1960 ◽  
Vol 7 (1) ◽  
pp. 108-114 ◽  
Author(s):  
Robert R. Long
Keyword(s):  
Magnetic Field ◽  
Differential Equation ◽  
Partial Differential Equation ◽  
Steady Motion ◽  
Basic Flow ◽  
Primitive Equations ◽  
Order Partial Differential Equation ◽  
Conducting Liquid ◽  
Short Discussion ◽  
Special Case

In certain cases of steady motion of a conducting fluid in a magnetic field, the primitive equations may be integrated once, yielding a second-order partial differential equation in the stream function. This equation is highly non-linear in general, but for certain choices of basic flow and magnetic fields it is tractable. Several arbitrary functions of integration have to be evaluated to make the analysis useful. This may be done in a region that remains undisturbed. A short discussion is given to suggest a procedure for deciding in a special case whether this undisturbed region is ‘upstream’ or ‘downstream’.

Two Dimensional Matching

1997 ◽  
Author(s):  
A. Amir ◽  
M. Farach
Keyword(s):  
Pattern Matching ◽  
String Matching ◽  
Higher Dimensions ◽  
Natural Generalization ◽  
Theoretical Problem ◽  
Two Dimensional ◽  
Exact Matching ◽  
Matching Problem ◽  
Deterministic Algorithms ◽  
Special Case

String matching is a basic theoretical problem in computer science, but has been useful in implementating various text editing tasks. The explosion of multimedia requires an appropriate generalization of string matching to higher dimensions. The first natural generalization is that of seeking the occurrences of a pattern in a text where both pattern arid text are rectangles. The last few years saw a tremendous activity in two dimensional pattern matching algorithms. We naturally had to limit the amount of information that entered this chapter. We chose to concentrate on serial deterministic algorithms for some of the basic issues of two dimensional matching. Throughout this chapter we define our problems in terms of squares rather than rectangles, however, all results presented easily generalize to rectangles. The Exact Two Dimensional Matching Problem is defined as follows: . . . INPUT: Text array T[n x n] and pattern array P[m x m]. OUTPUT: All locations [i,j] in T where there is an occurrence of P, i.e. T[i+k+,j+l] = P[k+1,l+1] 0 ≤ k, l ≤ n-1. . . . A natural way of solving any generalized problem is by reducing it to a special case whose solution is known. It is therefore not surprising that most solutions to the two dimensional exact matching problem use exact string matching algorithms in one way or another. In this section, we present an algorithm for two dimensional matching which relies on reducing a matrix of characters into a one dimensional array. Let P' [1 . . .m] be a pattern which is derived from P by setting P' [i] = P[i,l]P[i,2]…P[i,m], that is, the ith character of P' is the ith row of P. Let Ti[l . . .n — m + 1], for 1 ≤ i ≤ n, be a set of arrays such that Ti[j] = T[i, j] T [ i , j + 1 ] • • • T[i, j + m-1]. Clearly, P occurs at T[i, j] iff P' occurs at Ti[j].

Existence and positivity of the limit in processes with a branching structure

1999 ◽  
Vol 36 (01) ◽  
pp. 132-138
Author(s):  
M. P. Quine ◽  
W. Szczotka
Keyword(s):  
Stochastic Process ◽  
Branching Process ◽  
Random Variables ◽  
Random Variable ◽  
Natural Generalization ◽  
Partial Sums ◽  
Urn Model ◽  
Special Case ◽  
Independent And Identically Distributed

We define a stochastic process {X n } based on partial sums of a sequence of integer-valued random variables (K 0,K 1,…). The process can be represented as an urn model, which is a natural generalization of a gambling model used in the first published exposition of the criticality theorem of the classical branching process. A special case of the process is also of interest in the context of a self-annihilating branching process. Our main result is that when (K 1,K 2,…) are independent and identically distributed, with mean a ∊ (1,∞), there exist constants {c n } with c n+1/c n → a as n → ∞ such that X n /c n converges almost surely to a finite random variable which is positive on the event {X n ↛ 0}. The result is extended to the case of exchangeable summands.

Differential Operators of infinite order

1980 ◽  
Vol 86 (1-2) ◽  
pp. 85-101
Author(s):  
Einar Hille
Keyword(s):  
Boundary Value Problems ◽  
Differential Operators ◽  
Linear Differential Operator ◽  
Boundary Value ◽  
Natural Generalization ◽  
Singular Boundary ◽  
Singular Boundary Value Problems ◽  
Linear Differential ◽  
Image Position ◽  
Special Case

SynopsisThe differential operators in question are of the form G(DZ) where G(w)is an entire function of order at most 1/n and minimal type while Dz is a linear differential operator of order n with coefficients which are entire ( = integral) functions of z, usually polynomials. This class of operators form a natural generalization of the class G(d/dz) studied during the first half of the century Muggli, Polya, Ritt and others. The class G(DZ) was introduced by the present author and his pupils in the 1940s. In fact, the present paper is partly based on a MS from that period, mostly devoted to the special casebut also containing generalizations, some of which were later worked out by Klimczak. A basic tool in this paper is the characteristic seriesExamples are given showing that the domain of absolute convergence of such a series need neither be convex nor of finite connectivity, a question which has puzzled the author for forty odd years. Characteristic series arising from regular or singular boundary value problems for the operator Dz are used to study the inversion problemfor given F(z). In particular it is shown that exp (Dx)[W(z)] = 0 has the unique solution W(z) ≡ 0. Some singular boundary value problems are considered briefly.

Extreme self-sacrifice beyond fusion: Moral expansiveness and the special case of allyship

2018 ◽  
Vol 41 ◽  
Author(s):  
Daniel Crimston ◽  
Matthew J. Hornsey
Keyword(s):  
General Theory ◽  
Biological Markers ◽  
Natural Environment ◽  
Relevant Dimension ◽  
Special Case

AbstractAs a general theory of extreme self-sacrifice, Whitehouse's article misses one relevant dimension: people's willingness to fight and die in support of entities not bound by biological markers or ancestral kinship (allyship). We discuss research on moral expansiveness, which highlights individuals’ capacity to self-sacrifice for targets that lie outside traditional in-group markers, including racial out-groups, animals, and the natural environment.

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